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On equilibrium problems. (English) Zbl 1064.49009
Summary: Some iterative methods for solving equilibrium problems are suggested and analyzed by using the technique of the auxiliary principle. We have shown that the convergence of the proposed methods either requires only pseudomonotonicity, which is a weaker condition than monotonicity or partially relaxed strongly monotonicity. Our results represent an improvement and refinement of previously known results. Since the equilibrium problems include variational inequalities and complementarity problems as special cases, the results proved in this paper continue to hold for these problems.

MSC:
49J40 Variational inequalities
47N10 Applications of operator theory in optimization, convex analysis, mathematical programming, economics
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
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